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Multilevel modeling of complex survey data

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  • Sophia Rabe-Hesketh

    (University of California, Berkeley)

Abstract

Survey data are often analyzed using multilevel or hierarchical models. For example, in education surveys, schools may be sampled at the first stage and students at the second stage and multilevel models used to model within-school and between-school variability. An important aspect of most surveys that is often ignored in multilevel modeling is that units at each stage are sampled with unequal probabilities. Standard maximum likelihood estimation can be modified to take the sampling probabilities into account, yielding pseudomaximum likelihood estimation, which is typically combined with robust standard errors based on the sandwich estimator. This approach is implemented in gllamm. I will introduce the ideas, discuss issues that arise such as the scaling of the weights, and illustrate the approach by applying it to data from the Program for International Student Assessment (PISA).

Suggested Citation

  • Sophia Rabe-Hesketh, 2007. "Multilevel modeling of complex survey data," West Coast Stata Users' Group Meetings 2007 14, Stata Users Group.
  • Handle: RePEc:boc:wsug07:14
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    File URL: http://repec.org/wcsug2007/stata_sophia.pdf
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    References listed on IDEAS

    as
    1. Germán Rodríguez & Noreen Goldman, 2001. "Improved estimation procedures for multilevel models with binary response: a case-study," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 164(2), pages 339-355.
    2. repec:bla:jorssa:v:158:y:1995:i:1:p:73-89 is not listed on IDEAS
    3. Anders Skrondal & Sophia Rabe-Hesketh, 2003. "Multilevel logistic regression for polytomous data and rankings," Psychometrika, Springer;The Psychometric Society, vol. 68(2), pages 267-287, June.
    4. Edward L. Korn & Barry I. Graubard, 2003. "Estimating variance components by using survey data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 175-190, February.
    5. S. Rabe-Hesketh & A. Skrondal, 2001. "Parameterization of Multivariate Random Effects Models for Categorical Data," Biometrics, The International Biometric Society, vol. 57(4), pages 1256-1263, December.
    6. Ganzeboom, H.B.G. & de Graaf, P.M. & Treiman, D.J. & de Leeuw, J., 1992. "A standard international socio-economic index of occupational status," WORC Paper 85970031-d601-46e3-befb-1, Tilburg University, Work and Organization Research Centre.
    7. Rabe-Hesketh, Sophia & Skrondal, Anders & Pickles, Andrew, 2005. "Maximum likelihood estimation of limited and discrete dependent variable models with nested random effects," Journal of Econometrics, Elsevier, vol. 128(2), pages 301-323, October.
    8. Anders Skrondal & Sophia Rabe-Hesketh, 2007. "Latent Variable Modelling: A Survey," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(4), pages 712-745.
    9. Sophia Rabe-Hesketh & Anders Skrondal & Andrew Pickles, 2004. "Generalized multilevel structural equation modeling," Psychometrika, Springer;The Psychometric Society, vol. 69(2), pages 167-190, June.
    10. Thomas Warm, 1989. "Weighted likelihood estimation of ability in item response theory," Psychometrika, Springer;The Psychometric Society, vol. 54(3), pages 427-450, September.
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